Following up this comment recently posted to Bio-Soft, on the matter
of curve-fitting sums of exponentials....
> Be careful. Fitting general sums of decaying exponentials is an
> ill-conditioned problem for which one is usually cautioned against
> general least-squares routines.
Hmm, is it possible that some of the ill-conditioning arises from
the application of straightforward least-squares itself? Or is the
ill-conditioning completely intrinsic to the sum-of-exponentials
model itself? In any event, a variant approach to this curve-fitting
problem has received attention in recent years, and it is claimed to
have certain advantages over the usual approach:
Herbert R. Halvorson (1992)
Pade'-Laplace algorithm for sums of exponentials: Selecting
appropriate exponential model and initial estimates
for exponential fitting
in, "Numerical Computer Methods"
Ludwig Brand & Michael L. Johnson, eds.
Methods in Enzymology 210: 54-67
E. Yeramian & P. Claverie (1987)
Analysis of multiexponential functions without a hypothesis
as to the number of components
Nature (12 March 1987) 326: 169-174
P. Claverie & A. Denis (1989)
[I don't know the title]
Computer Physics Reports 9(5): 247-299
[contains details of Claverie et al's Pade'-Laplace approach
to fitting sums of exponentials]
I cannot assure anybody of this alternate approach's merit, as my
awareness of it is only superficial. Still, it seems to be relevant
and may be worthy of investigation.
Mark Reboul
Columbia-Presbyterian Cancer Center Computing Facility
mark at cuccfa.ccc.columbia.edu